The present invention relates generally to controlling tension in a continuous material web and, more particularly, to a system and method for controlling tension in a continuous material web in which the system damping is improved and thus better tension responses are achieved.
The production and processing of strip and sheet materials, i.e., “web handling applications,” is actively used in many fields, such as web printing, newspaper pressing, and so on. In such web handling applications, it is a basic requirement that a web of material is produced to a specification which typically includes at least a predetermined thickness and predetermined material properties. To achieve such predetermined requirements, any mechanical forces applied to the web during processing must be accurately controlled. A transfer roll that conveys strip material from one part of a process to another must convey the web material while exerting a controlled tension or pressure that is accurately controlled and evenly distributed over the width of the roll.
In controlling mechanical forces applied to the web, the most important requirement is to make the tension and the linear velocity of the system stable. Thus, quite a few tension control methods have been proposed, such as conventional Proportional-Integral (PI) control, fuzzy self-adaptive Proportional-Integral-Derivative (PID) control, and active disturbance rejection control, for example. Conventional PI control methods are mainly based on torque regulated or speed regulated control. FIGS. 1A and 1B illustrate such torque regulated (1A) and speed regulated (1B) tension controls, respectively. As it can be seen, the toque regulated tension control technique consists of a torque current loop and a tension loop, while the speed regulated tension control technique not only has a torque current loop and a tension control loop, but also has an intermediate speed loop cascaded into the tension loop. From FIG. 1A, the second order open loop transfer function of the torque regulated tension control is obtained according to:
                                                        G              F                        ⁡                          (              s              )                                =                                                                      K                  p_F                                ⁡                                  (                                      1                    +                                                                  K                        i_F                                            s                                                        )                                            ⋆                              K                a                            ⋆                                                RK                  F                                                                                            JF                      t                                        ⁢                                          s                      2                                                        +                  Js                  +                                                            R                      2                                        ⁢                                          K                      F                                                                                            =                                                            K                  p_F                                ⁡                                  (                                      1                    +                                                                  K                        i_F                                            s                                                        )                                            ⋆                                                                    RK                    F                                    ⁢                                      K                    a                                                                                        JF                    t                                    ⁢                                      ω                    n                    2                                                              ⋆                                                ω                  n                  2                                                                      s                    2                                    +                                      2                    ⁢                                          ξω                      n                                        ⁢                    s                                    +                                      ω                    n                    2                                                                                      ,                            [                  Eqn          .                                          ⁢          1                ]            where, in FIG. 1A and [Eqn. 1], F* is the given tension, F is the actual tension, ωm′ is the actual speed of the main motor, ωm is the actual speed of the winder, GPI_F(z) is the PID of the tension loop, isq is the torque producing current, Ka is the proportionality coefficient between electromagnetic torque and torque current, KF is the tension constant in kN·s/m, Tm is the motor torque, GωmT is the transfer function between speed and torque, R is the real-time diameter of the winder, TL is the load torque, GFΔν is the dynamic transfer function of tension, ωn is the natural frequency, J is the rotational inertia of the winding block, r is the radius of the main motor, and Δν is a velocity difference between a speed near the main motor and a speed near the secondary motor.
From FIG. 1B, the speed regulated tension control is a third order system and is obtained according to:
                                                        G              F                        ⁡                          (              s              )                                =                                                    K                p_F                            ⁡                              (                                  1                  +                                                            K                      i_F                                        s                                                  )                                      ⋆                                                            K                  a                                ⁢                                  RK                                      p_                    ⁢                    ω                                                  ⁢                                                      K                    F                                    ⁡                                      (                                          s                      +                                              K                                                  i_                          ⁢                          ω                                                                                      )                                                                                                                    JF                    t                                    ⁢                                      s                    3                                                  +                                                      (                                          J                      +                                                                        K                          a                                                ⁢                                                  K                                                      p_                            ⁢                            ω                                                                          ⁢                                                  F                          t                                                                                      )                                    ⁢                                      s                    2                                                  +                                                      (                                                                                            R                          2                                                ⁢                                                  K                          F                                                                    +                                                                        K                          a                                                ⁢                                                  K                                                      p                            ω                                                                                              +                                                                        K                          a                                                ⁢                                                  K                                                      p                            _ω                                                                          ⁢                                                  K                                                      i                            _ω                                                                          ⁢                                                  F                          t                                                                                      )                                    ⁢                  s                                +                                                      K                    a                                    ⁢                                      K                                          p_                      ⁢                      ω                                                        ⁢                                      K                                          i                                              _                        ⁢                        ω                                                                                                                                ,                            [                  Eqn          .                                          ⁢          2                ]            where, in FIG. 1B and [Eqn. 2], F* is the given tension, F is the actual tension, ωm* is the given speed of the winder, ωm is the actual speed of the winder, GPI_F(z) is the PID of the tension loop, ωm′ is the actual speed of the main motor, {tilde over (ω)}m(k) is the sampling speed of the winder, GPI—ω(z) is the PID of speed loop, isq is the torque producing current, Ka is the proportionality coefficient between electromagnetic torque and torque current, KF is the tension constant in kN·s/m, Tm is the motor torque, GωmT is the transfer function between speed and torque, J is the rotational inertia of the winding block, R is the real-time diameter of the winder, TL is the load torque, GFΔν is the dynamic transfer function of tension, Gd is the delay of speed sampling, r is the radius of the main motor, and Δν is a velocity difference between a speed near the main motor and a speed near the secondary motor.
In order to have a good dynamic performance for tension control, Kp and Ki, of tension PI controller gains should be properly designed to achieve sufficient system gain and phase margins. However, it is recognized that the crossover frequency of torque regulated tension control is smaller than that of speed regulated tension control. The step response of torque regulated tension control tends to vibrate more easily because the crossover frequency of the torque regulated tension control system is limited by low damping of its natural resonant frequency. Although a derivation term can be added in PID control to achieve fast system tension response, it will introduce noise to the system. This small incurred noise may be acceptable in common continuous system; however, it is improper for systems with high control performance requirements, such as discontinuous systems. In the speed regulated tension control, the dynamic performance is improved by introducing the cascaded speed loop. However, the crossover frequency of this kind of tension loop is limited by the relatively low speed loop bandwidth, especially for systems with a large inertia.
It would therefore be desirable to provide a system and method for controlling tension in a continuous material web, with such a system and method providing a fast, dynamic system tension response with low vibration and low noise and useable with a variety of different systems, including systems with a large inertia.